The United States warned Monday that Russia would put at risk hopes for more constructive relations if it uses its UN veto to shut the sole border crossing for aid into Syria.

Secretary of State Antony Blinken joined Italy in leading talks in Rome of the US-led coalition to defeat the Islamic State group which discussed the Bab al-Hawa crossing into Syria from Turkey.

Blinken told reporters it was crucial to work to "broadening cross-border assistance, which is essential in reaching millions of Syrians who are in dire need of food, medicine, Covid vaccines and other lifesaving aid".

The crossing is due to close on July 10 without UN authorisation for another year and Russia -- which has already succeeded in reducing the border openings to one -- has not ruled out using its veto power to block an extension.

Russia and Iran are the chief supporters of President Bashar al-Assad -- who has wrested back control of most of Syria after a brutal decade-old civil war -- and say that Damascus as the sovereign power should have sole prerogative over aid deliveries.

A senior US official who accompanied Blinken said when asked about the Russian position: "Obviously we don't want any permanent UN Security Council member to veto that."

"What's been made clear all the way from the president all the way down to much lower-level officials to the Russians and to others is that we want to have a constructive relationship with Russia on the areas on which we can work together and we think Syria ought to be one of them," the official said.

"But the test is going to be whether or not we can maintain and expand these cross-border mechanisms," he said.

"If we're not able to work together on this basic human need, that would make it very difficult to work on anything else with the Russians with regard to Syria more broadly."

President Joe Biden raised the issue when he met on June 16 in Geneva with his Russian counterpart Vladimir Putin.

Both presidents had voiced hope that the summit would bring more stability to US-Russia relations after months of soaring tensions.

UN Secretary-General Antonio Guterres last week urged all Security Council nations to reach a consensus to preserve the crossing, which allows aid to reach some three million people living in the Idlib region.